No, expired infractions never count against you. However, if you accumulate enough, an S-mod might come around and simply outright ban you because you got so many infractions that they believe that you're not worth the trouble...

Referrals work like this: If a person registers on the forums, and they put your name down as the person who referred you here, you get one referral logged on your page. It has nothing to do with infractions, be they expired or not.

It's pretty simple, actually. It takes place in a different region with an undetermined set of Pokémon, and involves anything from being a king and handling diplomacy to fighting on the field, or doing something else.